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- Vladimír Janovský, Tomás Ligurský
- Mathematics and Computers in Simulation
- 2012

A discrete static contact problem with Coulomb friction is considered. The objective is to analyze non unique solutions. Since the model depends on parameters, we explore continuation (path-following) techniques for its numerical solution. In particular, we analyse a model with one and two contact nodes. © 2010 IMACS. Published by Elsevier B.V. All rights… (More)

- T. Ligurský
- 2008

The paper deals with a discrete model of a two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable. It is shown that a solution exists for any F and is unique if F is sufficiently small. We also prove that this unique solution is a Lipschitz continuous function of F . Numerical realization is… (More)

- Tomas Ligursky, Yves Renard, Tomáš Ligurskýa
- 2017

A continuation problem for finding successive solutions of discretised abstract first-order evolution problems is proposed and a general piecewise C1 continuation problem is studied. A condition ensuring local existence and uniqueness of its solution curves is given. An analogy of the first-order system of smooth problems is derived and results of existence… (More)

- Jaroslav Haslinger, Radek Kucera, Tomás Ligurský
- J. Computational Applied Mathematics
- 2011

This paper analyzes a discrete form of 3D contact problems with local orthotropic Coulomb friction and coefficients of friction which may depend on the solution itself. The analysis is based on the fixed-point reformulation of the original problem. Conditions guaranteeing the existence and uniqueness of discrete solutions are established. Finally, numerical… (More)

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